(Name,
address and telephone number of person authorized to receive notices and communications)

May 2, 2018

(Date
of event which requires filing of this statement)

If the
filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D,
and is filing this schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box.¨

(Continued on the following pages)

Note: Schedules filed in paper format shall include a signed
original and five copies of the schedule, including all exhibits. See Rule 13d-7 for other parties to whom copies are to be sent.

*The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing
information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall
not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or
otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however,
see the Notes).

CUSIP No. 45337C102

Page 2 of 13 Pages

1.

NAMES OF REPORTING PERSONS

Baker Bros. Advisors LP

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

(a) ¨

(b) ¨

3.

SEC USE ONLY

4.

SOURCE OF FUNDS*

OO

5.

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
TO ITEM 2(d) or 2(e)

(2) Based on 211,969,163 shares of the
Common Stock outstanding as of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the Securities and Exchange
Commission (“SEC”) on May 1, 2018 and 160,000 shares of Common Stock underlying 160,000 options.

CUSIP No. 45337C102

Page 3 of 13 Pages

1.

NAMES OF REPORTING PERSONS

Baker Bros. Advisors (GP) LLC

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

(a) o

(b) o

3.

SEC USE ONLY

4.

SOURCE OF FUNDS*

OO

5.

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
TO ITEM 2(d) or 2(e)

(1) Includes 160,000 shares of Common Stock underlying 160,000 options.

(2) Based on 211,969,163 shares of the
Common Stock outstanding as of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the SEC on May 1, 2018 and
160,000 shares of Common Stock underlying 160,000 options.

CUSIP No. 45337C102

Page 4 of 13 Pages

1.

NAMES OF REPORTING PERSONS

Julian C. Baker

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

(a)
o

(b)
o

3.

SEC USE ONLY

4.

SOURCE OF FUNDS*

OO

5.

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
TO ITEM 2(d) or 2(e)

(1) Includes 160,000 shares of Common Stock underlying 160,000 options.

(2) Based on 211,969,163 shares of the
Common Stock outstanding as of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the SEC on May 1, 2018 and
160,000 shares of Common Stock underlying 160,000 options.

CUSIP No. 45337C102

Page 5 of 13 Pages

1.

NAMES OF REPORTING PERSONS

Felix J. Baker

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

(a)
o

(b)
o

3.

SEC USE ONLY

4.

SOURCE OF FUNDS (See Instructions)

OO

5.

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
TO ITEM 2(d) or 2(e)

(1) Includes 160,000 shares of Common Stock underlying 160,000 options.

(2) Based on 211,969,163 shares of the
Common Stock outstanding as of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the SEC on May 1, 2018 and
160,000 shares of Common Stock underlying 160,000 options.

CUSIP No. 45337C102

Page 6 of 13 Pages

1.

NAMES OF REPORTING PERSONS

FBB2, LLC

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

(a)
o

(b)
o

3.

SEC USE ONLY

4.

SOURCE OF FUNDS (See Instructions)

OO

5.

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT
TO ITEM 2(d) or 2(e)

(1) Based on 211,969,163 shares of the
Common Stock outstanding as of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the SEC on May 1, 2018.

Amendment No. 21 to Schedule 13D

This Amendment No. 21 to Schedule 13D amends and supplements the
statements on the previously filed Schedule 13D, as amended, filed by Baker Bros. Advisors LP (the “Adviser”), Baker
Bros. Advisors (GP) LLC (the “Adviser GP”), Julian C. Baker, Felix J. Baker, FBB2, LLC (“FBB2”) and FBB
Associates (“FBB”) (collectively the “Reporting Persons”). Except as supplemented herein, such statements,
as hereto amended and supplemented, remain in full force and effect. Information given in response to each item shall be deemed
incorporated by reference in all other items, as applicable. Each capitalized term used but not defined herein has the meaning
ascribed to such term in the Schedule 13D, as amended.

The Adviser GP is the sole general partner of the Adviser. Pursuant
to management agreements, as amended, among the Adviser, Baker Brothers Life Sciences, L.P. (“Life Sciences”), 14159,
L.P. (“14159”), and 667, L.P. (“667”, and together with Life Sciences and 14159, the “Funds”),
and their respective general partners, the Funds’ respective general partners relinquished to the Adviser all discretion
and authority with respect to the investment and voting power of the securities held by the Funds, and thus the Adviser has complete
and unlimited discretion and authority with respect to the Funds’ investments and voting power over investments.

ITEM 2. Identity and Background.

(a) The Reporting Persons are:

1.

The Adviser

2.

The Adviser GP

3.

Felix J. Baker

4.

Julian C. Baker

5.

FBB2

6.

FBB

(b) The business address of each of the Reporting Persons is:

c/o Baker Bros. Advisors LP

860 Washington Street, 3rd Floor

New York, NY 10014

(c) The Adviser is an entity engaged in investment activities, and
the Adviser GP is in the business of acting as its general partner and, through the Adviser, investment activities. The principal
business of each of Julian C. Baker and Felix J. Baker is to serve as a managing member of the Adviser GP. The principal business
of FBB2 is to engage in investment activities. Julian C. Baker and Felix J. Baker are the sole managers of FBB2 and by policy
they do not transact in or vote the securities of Incyte Corporation (the “Issuer”) held by FBB2. The principal
business of FBB is to engage in investment activities. Julian C. Baker and Felix J. Baker are the sole general partners of
FBB.

(d) and (e) During the past five years, none of the Reporting Persons
nor any of the Funds (as defined below) has been (i) convicted in a criminal proceeding (excluding traffic violations or similar
misdemeanors) or (ii) a party to a civil proceeding of a judicial or administrative body of competent jurisdiction and as a result
of such proceeding was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating
activities subject to, federal or state securities laws or finding any violation with respect to such laws.

(f) The Adviser is a limited partnership organized under the laws
of the State of Delaware. The Adviser GP is a limited liability company organized under the laws of the State of Delaware. FBB2
is a limited liability company organized under the laws of the state of Delaware. FBB is a general partnership organized
under the laws of the state of New York. The citizenship of each of Julian C. Baker and Felix J. Baker is the United States
of America.

Item 3. Source and Amount of Funds or Other Consideration

Item 3 of Schedule 13D is supplemented and amended, as the case
may be, as follows:

The disclosure in Item 4 below is incorporated herein by reference.

Item4. Purpose of the Transaction.

Item 4 of Schedule 13D is supplemented and superseded, as the case
may be, as follows:

On May 2, 2018 the Adviser acquired beneficial ownership of 20,000
shares of common stock of Incyte Corporation (the “Issuer”), as a result of the exercise of 20,000 options to purchase
the Issuer’s common stock at $9.92 per share (the “Exercised Stock Options”) held directly by Julian C. Baker.
Julian C. Baker currently serves on the Issuer’s Board of Directors (the “Board”) as a representative of the
Funds. The policy of the Funds and the Adviser does not permit principals or full-time employees of the Adviser to receive compensation
for serving as directors of the Issuer, and the Funds are instead entitled to the pecuniary interest in the Exercised Stock Options.
Julian C. Baker, as an agent in his capacity as a director of the Issuer, entered into a proceeds agreement (the “Proceeds
Agreement”) with the Adviser on May 2, 2018. Pursuant to the Proceeds Agreement, Julian C. Baker agreed that, with respect
to the Exercised Stock Options and the common stock received as a result of the exercise of the Exercised Stock Options (the “Common
Stock”) on May 2, 2018, the Adviser will have dispositive power as well as the ability to control the timing of exercise
of the Exercised Stock Options and that any proceeds from the sale of the Common Stock will be remitted to the Adviser net of brokerage
commissions. Other than through their control of the Adviser, Felix J. Baker and Julian C. Baker have neither voting nor dispositive
power and have no direct pecuniary interest in the Exercised Stock Options or the Common Stock. Pursuant to the Proceeds Agreement,
the Adviser funded Julian C. Baker’s exercise of the Exercised Stock Options through loans from the Funds (the “Loan
Agreements”). The total amount expended on acquiring the Common Stock was $198,400.

In order to affect the exercise of the Exercised Stock Options,
on May 2, 2018, the Adviser entered into the Loan Agreements with the Funds pursuant to which 667, Life Sciences and 14159 loaned
$24,936.17, $169,437.49 and $4,026.34, respectively, totaling $198,400 to the Adviser for the purpose of acquiring the Common Stock.
The loan is due May 2, 2048, or earlier if the Common Stock are sold (“Due Date”), with interest payable through the
Due Date at a rate of 2.94% annually.

On March 29, 2018 Julian C. Baker received 228 shares of Common
Stock in lieu of quarterly cash director’s compensation. Julian C. Baker is a Director of the Issuer.

On May 1, 2018, Julian C. Baker was granted 15,000 Stock Options
(as defined below) at an exercise price of $60.85 which vest on the first anniversary of the grant date or, if earlier, the date
of the next regular annual meeting of the Issuer stockholders or upon a change in control of the Issuer (as defined in the Issuer's
Amended and Restated 2010 Stock Incentive Plan) and expire on April 30, 2028. In connection with his service on the Issuer’s
Board, Julian C. Baker holds options to purchase Common Stock of the Issuer (“Stock Options”), Common Stock and Common
Stock received from the exercise of Stock Options as disclosed in previous amendments to this Schedule 13D.

Julian C. Baker serves on the Board as a representative of the Funds.
The policy of the Funds and the Adviser does not permit principals or
full-time employees or principals of the Adviser to receive compensation for serving as a director of the Issuer. Therefore, Julian
C. Baker has no pecuniary interest in the Stock Options, Common Stock or Common Stock received from the exercise of Stock Options
received as directors’ compensation. The Funds are instead entitled to the pecuniary interest in the Stock Options, Common
Stock and Common Stock received from the exercise of Stock Options received as directors’ compensation.

The Adviser has voting and investment power over the Stock
Options, Common Stock and Common Stock underlying such Stock Options and Common Stock received from the exercise of Stock
Options by Julian C. Baker received as directors’ compensation. The
Adviser GP, and Felix J. Baker and Julian C. Baker as principals of the Adviser GP, may be deemed to have the power to vote or
direct the vote of and the power to dispose or direct the disposition of the Stock Options, Common Stock, Common Stock received
from the exercise of Stock Options and Common Stock underlying such Stock Options held by Julian C. Baker received as directors
compensation.

The Funds hold securities of the Issuer for investment purposes.
The Reporting Persons or their affiliates may purchase additional securities of the Issuer or dispose of securities in varying
amounts and at varying times depending upon the Reporting Persons’ continuing assessments of pertinent factors, including
the availability of shares of Common Stock or other securities for purchase at particular price levels, the business prospects
of the Issuer, other business investment opportunities, economic conditions, stock market conditions, money market conditions,
the attitudes and actions of the Board of Directors and management of the Issuer, the availability and nature of opportunities
to dispose of securities of the Issuer and other plans and requirements of the particular persons. The Reporting Persons may discuss
items of mutual interest with the Issuer, which could include items in subparagraphs (a) through (j) of Item 4 of Schedule 13D.

Depending upon their assessments of the above factors, the Reporting
Persons or their affiliates may change their present intentions as stated above and they may make suggestions to the management
of the Issuer regarding financing, and may acquire additional securities of the Issuer, including shares of Common Stock (by means
of open market purchases, privately negotiated purchases, exercise of some or all of the Stock Options (as defined above), or otherwise)
or may dispose of some or all of the securities of the Issuer, including shares of Common Stock, under their control.

Except as otherwise disclosed herein, at the present time, the Reporting
Persons do not have any plans or proposals with respect to any extraordinary corporate transaction involving the Issuer including,
without limitation, those matters described in subparagraphs (a) through (j) of Item 4 of Schedule 13D.

Item
5. Interest in Securities of the Issuer.

(a) and (b) Items 7 through 11 and 13 of
each of the cover pages of this Amendment No. 21 are incorporated herein by reference. Set forth below is the aggregate number
of shares of Common Stock directly held by each of the Funds and the percentage of the Issuer’s outstanding shares of Common
Stock such holdings represent. The information set forth below is based on 211,969,163 shares of the Common Stock outstanding as
of April 24, 2018, as reported in the Issuer’s Form 10-Q filed with the SEC on May 1, 2018. Such percentage figures are calculated
in accordance with Rule 13d-3 under the Securities Exchange Act of 1934, as amended.

Shares of Common

Percent of Class

Holder

Stock

Outstanding

667, L.P.

4,290,108

2.0

%

Baker Brothers Life Sciences, L.P.

29,150,637

13.8

%

14159, L.P.

692,706

0.3

%

Total

34,133,451

16.1

%

The Adviser GP, Felix J. Baker and Julian C. Baker as principals
of the Adviser GP, and the Adviser may be deemed to be beneficial owners of securities of the Issuer directly held by the Funds,
and may be deemed to have the power to vote or direct the vote of and the power to dispose or direct the disposition of such securities.

Each of the Adviser, the Adviser GP, Felix J. Baker and Julian
C. Baker disclaims beneficial ownership of the securities held by each of the Funds, and this Amendment No. 21 shall not be deemed
an admission that any of the Adviser, the Adviser GP, Felix J. Baker or Julian C. Baker is the beneficial owners of such securities
for purposes of Section 13(d) or for any other purpose, except to the extent that any such Reporting Persons actually exercises
voting or dispositive power with respect to such securities.

Julian C. Baker and Felix J. Baker are also the sole managers of
FBB2 and by policy they do not transact in or vote the securities of the Issuer held by FBB2.

Julian C. Baker and Felix J. Baker are also the sole partners of
FBB and as such may be deemed to be beneficial owners of securities owned by FBB and may be deemed to have the power to vote or
direct the vote and dispose or direct the disposition of those securities.

(c) Except as disclosed herein or in any previous amendments to
this Schedule 13D, none of the Reporting Persons or their affiliates has effected any other transactions in securities of the Issuer
during the past 60 days.

(d) Certain securities of the Issuer are held directly by 667, a
limited partnership the sole general partner of which is Baker Biotech Capital, L.P., a limited partnership the sole general partner
of which is Baker Biotech Capital (GP), LLC. Julian C. Baker and Felix J. Baker are the controlling members of Baker Biotech Capital
(GP), LLC.

Certain securities of the Issuer are held directly by Life Sciences,
a limited partnership the sole general partner of which is Baker Brothers Life Sciences Capital, L.P., a limited partnership the
sole general partner of which is Baker Brothers Life Sciences Capital (GP), LLC. Julian C. Baker and Felix J. Baker are the controlling
members of Baker Brothers Life Sciences Capital (GP), LLC.

Certain securities of the Issuer are held directly by 14159, a limited
partnership the sole general partner of which is 14159 Capital, L.P., a limited partnership the sole general partner of which is
14159 Capital (GP), LLC. Julian C. Baker and Felix J. Baker are the controlling members of 14159 Capital (GP), LLC.

(e) Not applicable.

Item 6. Contracts, Arrangements, Understandings or Relationships
with Respect to the Securities of the Issuer.

Item 6 of this Schedule 13D is hereby supplemented and amended,
as the case may be, as follows:

The disclosure in Item 4 is incorporated
by reference herein.

The Loan Agreement and the Proceeds Agreement are filed as Exhibits
99.1 and 99.2, respectively, and are incorporated by reference herein.

Item 7. Material to be Filed as Exhibits.

Exhibit

Description

99.1

Loan Agreement, dated May 2, 2018, by and among the Adviser and the Funds.

99.2

Proceeds Agreement, dated May 2, 2018, by and between the Adviser and Julian C. Baker.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief,
I certify that the information set forth in this statement is true, complete and correct.

For value received, Baker Bros Advisors LP (the “Management
Company”) promises to pay Baker Brothers Life Sciences, L.P., 667, L.P., and 14159, L.P., (collectively “The Funds”),
the amounts set forth in Schedule A below, payable on the Due Date (as defined below) with interest payable through the Due Date
at a rate of 2.94% annually.

The Funds are lending the Management Company these amounts so that
Julian Baker, as agent of the Management Company, may exercise 20,000 Incyte Corporation (“INCY”) Director’s
Non-qualified Stock Options at $9.92 per share (the “Shares”) and deposit the Shares into Julian Baker’s brokerage
account held at JPMorgan.

The “Due Date” shall be May 2, 2048, however, following
the sale by Julian Baker of all of the Shares, the Due Date shall accelerate to the date that is 10 days after date of the last
sale of Shares.

This Loan Agreement shall be construed in accordance with the laws
of the State of New York.

Baker Bros. Advisors
LP

/s/ Alexandra A. Toohey

/s/ Alexandra A. Toohey

By: Alexandra A. Toohey, Chief Financial Officer

667, L.P.

By:
Baker Bros. Advisors LP, management company and investment adviser to 667, L.P., pursuant
to authority granted
to it by Baker Biotech Capital, L.P., general partner to 667, L.P., and not as the general partner.

/s/ Scott L. Lessing

Scott Lessing

President

1

BAKER BROTHERS LIFE SCIENCES, L.P.

By: BAKER BROS. ADVISORS LP, ,
management company and investment adviser to Baker Brothers Life Sciences, L.P., pursuant to authority granted to it by
Baker Brothers Life Sciences Capital, L.P., general partner to Baker Brothers Life Sciences, L.P., and not as the general partner.

/s/ Scott L. Lessing

Scott Lessing

President

14159,
L.P.,

By: Baker
Bros. Advisors LP, management company and investment adviser to 14159, L.P., pursuant to authority granted to
it by 14159 Capital, L.P., general partner to 14159, L.P., and not as the general partner.

/s/ Scott L. Lessing

Scott Lessing

President

Schedule A

Fund

667, L.P.

Baker Brothers Life Sciences, L.P.

14159, L.P.

Total

Loan

$

24,936.17

$

169,437.49

$

4,026.34

$

198,400.00

2

Exhibit 99.2

PROCEEDS AGREEMENT

AGREEMENT dated as of May 2, 2018 by
and between Baker Bros. Advisors LP (the “Management Company”) and Julian Baker (the “Agent”).

WHEREAS, the Agent, in his capacity as
a director of Incyte Corporation (the “Company”), received non-transferable options (the “Options”) to
purchase 20,000 shares of the Company common stock (the “Stock”) according to the below Schedule A;

WHEREAS, the Management Company provides
management and administrative service to each of Baker Brothers Life Sciences, L.P., 667, L.P., and 14159, L.P. (the “Funds”)
in exchange for a management fee from each (the “Management Fees”);

WHEREAS, the Company is a portfolio company
of the Funds;

WHEREAS, Pursuant to the Funds’
Limited Partnership Agreements and the Management Company’s policies, directors’ fees, consulting fees and other remuneration
(including options, warrants or other equity securities) paid by Funds portfolio companies to an agent, officer or employee of
the Management Company shall reduce (but not below $0) the Management Fees; and

WHEREAS, the Agent and the Management
Company wish to memorialize their understanding with respect to the Options;

NOW, THEREFORE, for good and valuable
consideration, the parties
agree as follows:

1. Subject
to the provisions of Section 2, the Agent agrees, as soon as practicable after receipt from the Company, to remit to the Management
Company any directors’ fees, consulting fees and other remuneration that the Agent receives from the Company.

2. The
Agent shall exercise the Options at the time directed by the Management Company. When the Agent exercises the Options, the Management
Company shall provide the Agent with the amount of cash necessary to enable the Agent to purchase the Stock for which the Options
are being exercised from the Company, in compliance with the terms of the Options.

3. Thereafter,
the Agent shall hold the Stock in a brokerage account at JPMorgan which is not commingled with other personal holdings of the Agent
until directed by the Management Company to sell the Stock. The Agent agrees, as soon as practicable after receiving direction
from the Management Company, to sell all, or any portion, of the Stock as directed by the Management Company and to remit the gross
cash proceeds (but net of brokerage commissions) from the sale of the Stock to the Management Company.

4. The
Agent agrees not to amend or modify the Options, waive any of the provisions thereof, or enter into any agreement or understanding
with respect to the Options or the Stock, without the prior written consent of the Management Company.

5. The
Agent shall not report any income attributable to these transactions as his own income, but instead, shall report such income on
any and all tax returns required to be filed by the Agent as received by him only in his capacity as an agent, officer or employee
of the Management Company. The Management Company shall report all such income on any and all tax returns required to be filed
by the Management Company.

6. This
Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective heirs, legal representatives,
successors and assigns. This Agreement shall survive the death, merger, dissolution or termination of any of the parties hereto
and shall continue in full force and effect notwithstanding that the Agent shall cease to be an agent, officer or employee of the
Management Company for any reason.

7. This
Agreement may be amended or modified only by a writing signed on behalf of the parties hereto. No provision of this Agreement may
be waived except in writing signed on behalf of the party against whom such waiver is asserted.

8. From
and after the date of this Agreement, the parties shall execute and deliver such instruments, documents and other writings, and
take such other actions, as may be necessary to confirm and carry out and to effectuate fully the intent and purposes of the transactions
on their part respectively contemplated by this Agreement.

9. If
any of the benefits contemplated by this Agreement would be reduced or unachievable because of restrictions or prohibitions imposed
by law (by way of example only, the Securities Act of 1933, state securities laws, or the Company’s governing instruments),
the parties hereto shall use their best efforts to preserve the intent of this Agreement and the benefits contemplated hereby by
amending, modifying or waiving in an appropriate manner the provisions of this Agreement.

10. This
Agreement shall be governed by and construed in accordance with the laws of the State of New York.

IN WITNESS WHEREOF, the undersigned have
executed this Proceeds Agreement as of the date first above written.